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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.pol_ref.precision_pol"></a><a class="link" href="precision_pol.html" title="Precision Policies">Precision Policies</a>
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<p>
        There are two equivalent policies that effect the <span class="emphasis"><em>working precision</em></span>
        used to calculate results, these policies both default to 0 - meaning calculate
        to the maximum precision available in the type being used - but can be set
        to other values to cause lower levels of precision to be used. One might
        want to trade precision for evaluation speed.
      </p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
<span class="identifier">digits10</span><span class="special">;</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
<span class="identifier">digits2</span><span class="special">;</span>

<span class="special">}}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
        As you would expect, <span class="emphasis"><em>digits10</em></span> specifies the number of
        decimal digits to use, and <span class="emphasis"><em>digits2</em></span> the number of binary
        digits. Internally, whichever is used, the precision is always converted
        to <span class="emphasis"><em>binary digits</em></span>.
      </p>
<p>
        These policies are specified at compile-time, because many of the special
        functions use compile-time-dispatch to select which approximation to use
        based on the precision requested and the numeric type being used.
      </p>
<p>
        For example we could calculate <code class="computeroutput"><span class="identifier">tgamma</span></code>
        to approximately 5 decimal digits using:
      </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits10</span><span class="special">;</span>

<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">my_pol_5</span><span class="special">;</span> <span class="comment">// Define a new, non-default, policy</span>
<span class="comment">// to calculate tgamma to accuracy of approximately 5 decimal digits.</span>
</pre>
<p>
        Or again using helper function <code class="computeroutput"><span class="identifier">make_policy</span></code>:
      </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">;</span>

<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>

<span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;());</span>  <span class="comment">// Concise make_policy.</span>
</pre>
<p>
        And for a quantile of a distribution to approximately 25-bit precision:
      </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">;</span>

<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>

<span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">bits</span> <span class="special">=</span> <span class="number">25</span><span class="special">;</span> <span class="comment">// approximate precision.</span>

<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span>
      <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">bits</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;(),</span>
      <span class="number">0.05</span><span class="special">);</span> <span class="comment">// 5% quantile.</span>
</pre>
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